What's Our Real Trade Deficit With China?

Is our trade deficit with China exaggerated? The Wall Street Journal reports on the difference between accounting for the entire value of finished goods that are imported from China vs. only the value-added of the goods imported from China:

A study by the Sloan Foundation in 2007, for example, found that only $4 of an iPod that costs $150 to produce is made in China, even though the final assembly and export occurs in China. The remaining $146 represents parts imported to China. If only the value added by manufacturers in China were counted, the real U.S.-China trade deficit would be as much as 30% lower than last year's gap of at $226.8 billion, according to a number of economists.

At the same time, the U.S. trade deficit with Japan would have been 25% higher than the $44.8 billion reported last year, because many goods that China and others export to the U.S. contain parts purchased in Japan.

....But it is a tough nut to crack. Economists can look up, for example, that China exported 52,176 metric tons of screws, bolts and nuts to South Korea in 2009, according to Global Trade Information Services, a consultancy based in Geneva. But they can't trace those pieces to figure out if they wound up in exported products.

Experts also don't agree on what should be considered an intermediate good. Should the imported fuel used to power the factory be counted? What about the consultant flown in from London?